Probing Charge Generation Efficiency in Thin-Film Solar Cells by Integral-Mode Transient Charge Extraction

The photogeneration of free charges in light-harvesting devices is a multistep process, which can be challenging to probe due to the complexity of contributing energetic states and the competitive character of different driving mechanisms. In this contribution, we advance a technique, integral-mode transient charge extraction (ITCE), to probe these processes in thin-film solar cells. ITCE combines capacitance measurements with the integral-mode time-of-flight method in the low intensity regime of sandwich-type thin-film devices and allows for the sensitive determination of photogenerated charge-carrier densities. We verify the theoretical framework of our method by drift-diffusion simulations and demonstrate the applicability of ITCE to organic and perovskite semiconductor-based thin-film solar cells. Furthermore, we examine the field dependence of charge generation efficiency and find our ITCE results to be in excellent agreement with those obtained via time-delayed collection field measurements conducted on the same devices.

O rganic semiconductors are characterized by incomplete free charge carrier generation at room temperature, which is directly related to their excitonic nature by a virtue of their low permittivity and thus incomplete screening of the electron−hole Coulomb force. To improve the charge generation efficiency, bulk heterojunctions (BHJ) comprising electron-donating (donor, D) and -accepting (acceptor, A) organic semiconductors are employed as the photoactive material in so-called BHJ organic solar cells (OSC). Free charge generation in these semiconductors ordinarily involves multiple steps starting with the photogeneration of singlet excitons in either the D or the A domains, followed by exciton diffusion to the D/A interface. At the D/A interface, excitons can undergo charge transfer (i.e., electron transfer from D to A or hole transfer from A to D) and form interfacial chargetransfer (CT) states, 1,2 comprising Coulombically bound donor cations and acceptor anions. The charge transfer process (sometimes referred to as charge generation) is believed to be independent of any applied external electric field and predominantly energetically and kinetically driven. 3 This mechanism can create photovoltage as the chemical potential of CT states becomes nonzero after charge generation, 4 but it does not necessarily result in a considerable photocurrent. Efficient generation of free charge carriers (essential for photocurrent) requires CT states to quickly dissociate to free charges before decaying back to the ground state. 5−7 However, the mechanism of CT state dissociation into free charges is still a matter of debate despite intensive studies over several decades. While the work of Braun 8 implied that CT dissociation in OSCs is field-dependent, most efficient D/A blends show either no or only weak dependence on the electric field. 9−12 Hence, more advanced models have been proposed to explain the fast and efficient dissociation of CT states to free charges. Clarke and Durrant, for instance, considered the role of entropy in CT dissociation events, 6 while other models include the role of energetic disorder, 13 delocalization, 14,15 and vibronically excited (i.e., "hot") states 16 in the formation of free, separated charges. The role of "hot CT states" was challenged by Kurpiers and co-workers, who found the electric field and temperature dependent charge generation in fullerene acceptor (FA)-based BHJs to be independent of excess energy. 12 They concluded, in line with past findings by Vandewal et al., 2 that charge generation proceeds through thermalized CT states, independent of activation energies and the energetic offset between relaxed singlet exciton and CT states. This is also to be expected in the new class of state-ofthe-art OSCs based on nonfullerene acceptors (NFA) exhibiting low energetic offsets. Despite this, recent studies on CT dissociation conducted on NFA systems suggested an electric field and excess energy dependent charge generation. 17 Furthermore, Karuthedath and co-workers proposed a model based on interfacial D/A band-bending inducing quadrupole moments, suggesting the requirement for an ionization energy offset to drive charge generation in both FA-and NFA-based OSCs. 18,19 To gain more insight into the process of CT state dissociation, methods capable of probing free charge generation efficiency in thin-film solar cells independent of bulk recombination are needed. This has proven to be challenging but, if successful, could guide a better understanding of the mechanism of charge generation in state-of-theart OSCs and thus aid molecular and architecture improvements. In the past, several measurement techniques have been employed to investigate free charge generation in optoelectronic devices. While intensity dependent photocurrent (IPC) 20 and external (internal) quantum efficiency [EQE (IQE)] 21−23 are prominent examples of steady-state techniques, transient absorption spectroscopy (TAS) 24−26 and timedelayed collection field (TDCF) are, in turn, commonly used time-resolved techniques. Probing charge generation using IPC is questionable, as the results can be affected by first-order losses due to trap-assisted recombination and the so-called pseudo-first-order recombination near the electrodes. 27,28 TAS, in turn, has been used to probe free charge generation via detecting geminate recombination at early time scales. 20, 29 However, TAS measurements are often performed in the transmission mode on thin films and not on fully optimized solar cell devices containing reflective back-electrodes. TDCF has been the most useful method and is frequently used to study the free charge generation dynamics in organic and perovskite solar cells. 12,30,31 However, while TDCF remains a powerful methodology, it uses a complex circuit requiring specialist current preamplifiers with fast bias ramp-up times and suffers from RC-time limitations at short time scales.
In this work we advance an alternative and potentially more straightforward measurement technique to probe charge generation in optoelectronic devices. The technique is based on an extension of the integral-mode time-of-flight method 32 in the low-intensity regime, which accounts for capacitive effects associated with the sandwich-type thin-film device structure. In contrast to TDCF, the proposed method does not suffer from limitations induced by RC effects, allows for a sensitive measurement of charge carrier density at very low pulse fluence without a reduced signal accuracy, and does not require ultrasensitive fast preamplifiers. The new method, however, has a more limited voltage range than TDCF. The analytical framework behind the technique, integral-mode transient charge extraction (ITCE), is derived and verified by drift-diffusion (DD) simulations. Finally, to demonstrate the method, we apply the technique to thin-film organic semiconductor and perovskite semiconductor (as a second verifying system) solar cells and probe the field-dependent external generation efficiency (EGE), finding good agreement of experimental results obtained via ITCE and TDCF conducted on the same devices.

■ METHODS AND MATERIALS
All devices were fabricated on ITO-patterned glass substrates (Lumtec). After cleaning the ITO substrates in DI water, acetone, and isopropanol, substrates were first dried by a  A Newport Oriel Sol2A simulator in combination with a Keithley 2400 source-measure unit was used for current density versus applied voltage (J−V) characterization. A KG3 filtered reference silicon cell (calibrated at the Fraunhofer ISE) was used to calibrate the solar simulator to the standard AM 1.5G condition (100 mW cm −2 ).
The schematic and circuit diagram of our ITCE method are shown in Figure 1a,b. Similar to the integral-mode time-offlight method, 32 a large load resistor and an external voltage source (to provide an external voltage V appl to the circuit) are connected in series with the device under test (DUT). However, to record the voltage across the device, an oscilloscope is configured in parallel to the DUT. A short laser pulse is used to generate charge carriers in the bulk of the DUT. A diode-pumped, Q-switched Nd:YAG laser (Quantel, Viron Version A) operating a 532 nm excitation wavelength, 6.84 ns pulse width, 0.04 μJ cm −2 pulse fluence, and 20 Hz repetition rate is used in combination with a Standa 10MVAA attenuator to generate charge carriers in the bulk of the DUT. A Keithley 2450 is used to apply voltages across the DUT, which is in series with a 1 MΩ load resistor. The voltage transients are recorded with an oscilloscope (Rohde and Schwarz, RTM 3004) with 1 MΩ input resistance in parallel with the DUT. For dark C−V measurements, an E5061B ENA Network Analyzer with modulation frequency of 1 kHz and a bandwidth of 10 Hz is used. The voltage drop across the DUT is measured by a Keithley 2450. Figure 1c,d schematically shows a simplified circuit and triggering diagrams of a typical TDCF experimental setup. Here, a variable prebias V pre is applied on the operational photovoltaic DUT using an external voltage source, while a short laser photopulse leads to the generation of charge carriers in the photoactive layer. After a certain delay time t delay , the photogenerated charges are extracted by applying a collection bias V coll (typically a high reverse bias). An oscilloscope is used to record the current flowing through the DUT, and by integrating the extraction photocurrent transient, the total number of extracted charge carriers can be obtained. More details of the TDCF setup are provided elsewhere. 34 ■ THEORY ITCE is based on connecting the sandwich-type thin-film diode or solar cell device in series with a large load resistance R L and a voltage source applying a DC bias V appl . The device is initially kept under DC conditions, with the corresponding voltage drop across the device being given by V dev = V appl − i 0 R L , where i 0 is the DC current through the circuit. At the time t = 0, a light pulse is applied to the device, resulting in charge carriers being generated inside the active layer. The photogenerated electrons and holes are subsequently transported under the influence of the internal electric field toward the cathode and anode, respectively, giving rise to a transient current i(t) and a voltage drop In general, with the anode assumed to be located at x = 0 and the cathode at x = d (d is the active layer thickness), the corresponding time-dependent current density j(t) = i(t)/A (where A is the device area) is independent of the position x in the device and given by 35 Here, E(x,t) is the electric field and j c (x,t) is the conduction current density given by the sum of the individual electron and hole current densities, which both on the other hand depend on the position x in the active layer and the time t; ε is the relative permittivity and ε 0 is the permittivity of the vacuum. Furthermore, the photoinduced change in the voltage drop Subsequently, upon taking the spatial average over the active layer of the total current in eq 1 and making use of eq 2, we obtain where Δi c (t) = (A/d)∫ 0 d j c (x,t) dx − i 0 is the change in the spatially averaged conduction currents induced by the light pulse (note that Δi c (t) = 0 for t < 0), while C A d geo 0 = εε is the geometrical capacitance of the active layer.
For large load resistances (R L C geo → ∞), eq 3 simplifies to ∂ΔV(t)/∂t = −Δi c (t)/C geo . Under these conditions, the maximal induced change in the voltage is given as ΔV max = ΔQ/C geo , where ΔQ = −∫ 0 t extr Δi c (t) dt is the total charge induced by the light pulse, while t extr is the time taken for all photogenerated charge carriers to be extracted at the electrodes. After accounting for nonuniform charge distributions, it can be shown that ΔQ is related to the charge carrier densities inside the active layer via 36 assuming negligible charge carrier recombination (i.e., low intensity condition) and no trapping during the extraction process (0 < t ≤ t extr ). Here, Δp(x) = p(x,0) − p(x,t extr ) and Δn(x) = n(x,0) − n(x,t extr ), where p(x,t) [n(x,t)] is the hole [electron] density within the active layer at position x and time t.

ACS Photonics
pubs.acs.org/journal/apchd5 Article In general, Δp(x) and Δn(x) can be expressed as Δp(x) = n ph (x) + Δp 0 (x) and Δn(x) = n ph (x) + Δn 0 (x), where n ph (x) is the initial photogenerated carrier density at t = 0 and Δp 0 (x) [Δn 0 (x)] is the related induced change in the dark background hole [electron] density inside the active layer. In the case of an undoped device with noninjecting contacts, the background densities are negligibly small, and the active layer may be treated as an insulator; for this simplified case, eq 4 reduces to ΔQ = C geo ΔV max = qn ̅ ph Ad, where n ̅ ph ≡ (1/d)∫ 0 d n ph (x) dx is the spatial average of the photogenerated carrier density at t = 0. However, most OSCs employ ohmic contacts. In these devices there exists a nonzero dark background density of electrons and holes, diffused from the contacts, accumulating near the cathode and anode contact, respectively. 38 These dark charge distributions near the contacts effectively reduce the thickness of the insulator-like region in the active layer, resulting in an increased device capacitance relative to C geo .
Accounting for the presence of dark charge carriers, eq 4 can be expressed as ΔQ = qn ̅ p h Ad − Δ Q 0 . Here, represents the corresponding charge induced by the difference between the background charge density profiles between t = 0 and t = t extr . However, since the background charge carrier profiles are determined by the prevailing applied voltage and electric field distribution (in contrast to the photogenerated charge qn ̅ ph Ad), ΔQ 0 is capacitive, associated with a redistribution of the background charge profiles induced by the voltage change ΔV max across the device. For small voltage perturbations ΔV max , we thus expect ΔQ 0 = (∂Q 0 /∂V)ΔV max . Provided that t extr ≪ R L C (large R L ), we then finally obtain is the voltage-dependent steady-state capacitance of the device in the dark at V = V dev . Hence, by measuring ΔV max via ITCE as a function of the voltage V dev across the device, in conjunction with dark device capacitance C, allows for n ̅ ph versus V dev to be calculated.
To verify the analytical treatment, we applied it to the result obtained from time-dependent DD simulations. The details of the DD model have been provided elsewhere. 38 Briefly, in the simulations, we assumed a trap-free and undoped active layer with a thickness of 100 nm, a dielectric constant ε = 3, balanced mobilities of 10 −4 cm 2 V −1 s −1 for electrons and holes, and a bimolecular recombination coefficient of β = 5 × 10 −12 cm 3 s −1 , corresponding to a Langevin reduction factor of ∼24. Further, a built-in voltage (V bi ) of 1.2 V and ohmic contacts that are perfectly selective for the extraction of electrons and holes at the cathode and anode contact, respectively, were assumed. The device was specified to have an electrical area of A = 0.04 cm 2 and connected in series with a large load resistance of R L = 1 MΩ. The corresponding geometric capacitance of the device is C geo ≈ 1.1 nF, amounting to an RC time of roughly 1 ms. Finally, the photogenerated carriers (introduced at t = 0) were taken to be generated with a uniform rate inside the active layer, with the corresponding density n ̅ ph = n ph assumed to be directly proportional to the pulse fluence. In this regard, geminate (first-order) recombination losses of excitons and chargetransfer states are assumed to be effectively included in n ph . To better demonstrate the capacitive effect, n ph was assumed to be independent of the electric field in the simulations. Figure 2a shows the simulated voltage transients (solid lines) for different V dev ranging between −1 V and 0.7 V. The corresponding ΔV max are plotted as a function of pulse fluence for different V dev in Figure 2b. In Figure 2c, on the other hand, the device capacitance C under steady-state conditions in the dark (corresponding to low frequencies) is simulated as a function of V dev . In general, it can be seen that ΔV max follows a linear dependence with the fluence at small ΔV max . At large enough fluences, however, ΔV max eventually deviates from linearity as both higher order recombination and screening of the prevailing electric field start to play a role (as ΔV max becomes comparable to V dev ). On the other hand, ΔV max is seen to strongly depend on V dev at low fluences. We note that this dependence is present even for the idealized case when no recombination of charge carriers is present (β = 0, dashed lines). Instead, the V dev dependence of ΔV max is a consequence of the associated induced redistribution of the dark background charge carrier profile inside the active layer. As V dev is increased, the diffusion of injected dark charges (from the

ACS Photonics
pubs.acs.org/journal/apchd5 Article electrodes) penetrates deeper into the bulk, effectively reducing the thickness of the neutral (insulator-like) region inside the active layer, manifest as an increased device capacitance relative to the geometrical capacitance C geo (cf. eq 6). Figure 2d shows the extracted charge carrier density n ph,extr , as obtained from the simulations using eq 5, relative to the input photogenerated carrier density n ph . Indeed, n ph,extr is closely given by n ph when the device capacitance C(V) ( Figure  2c) is used in eq 5. In contrast, if C = C geo is assumed instead, a deviation between n ph,extr and n ph is observed, resulting in an underestimation of the photogenerated carrier density by a factor of C/C geo . In devices with ohmic contacts (Figure 2c), this underestimation becomes strongly dependent on the voltage in the forward bias and may be mistaken as an apparent field dependence of EGE; hence, to correctly obtain n ph , the voltage dependence of the device capacitance must be accounted for. We note that there is a small deviation taking place between n ph,extr /n ph of the cases with and without recombination in the active layer at large V dev approaching the built-in voltage; this deviation can be attributed to additional (pseudo)first-order recombination taking place between photogenerated charge carriers and dark background charge carriers near the electrodes. 27,39 In principle, this additional loss may be minimized by tuning the optical electric field (e.g., careful choice of the laser wavelength or the introduction of optical spacer layer) such that the generation profile peaks in the middle of the active layer and is minimal near the electrodes. It should be stressed that, in the case of nonideal contacts, surface recombination (i.e., the collection of minority carriers at the "wrong" electrode) may become prevalent as well, presenting an additional voltage-dependent first-order recombination channel. 40 From the above presented theoretical and numerical analyses, we conclude that photogenerated charge carrier densities in thin-film solar cells can be measured sensitively via ITCE, when (i) higher-order recombination processes are not present, and (ii) (voltage dependent) carrier back-injection and diffusion-mediated redistribution of dark background charges in the photoactive layer of the DUT are accounted for. While (i) can be addressed by recording ITCE voltage transients at low pulse fluence and avoiding too high ΔV max (ΔV max should be as small as possible, preferably well below 10 mV), (ii) can be addressed by accurately measuring the voltage-dependent device capacitance (at low enough frequencies) in the dark. In the following, we will implement those findings and probe the EGE in different thin-film organic semiconductor and perovskite semiconductor solar cells.

■ RESULTS AND DISCUSSION
We first applied ITCE to the well-understood model organic solar cell, PCDTBT:PC 70 BM, to further validate the theoretical/numerical findings. Furthermore, we examined neat PCDTBT photovoltaic cells, as well as a high efficiency triple cation perovskite thin-film solar cells. We studied the field dependent EGE in these systems via ITCE and compared these data with benchmark TDCF results. To this end, EGE is evaluated as a function of V dev , noting that the (DC) electric field is expected to be uniform and scale linearly as E = (V dev − V bi )/d, with V bi on the order of 1 V in these devices. This is expected to be a good approximation for thin active layers and voltages well below V bi . Figure 3a shows the dark capacitances of all three devices plotted as a function of device voltage, V dev . As shown, the PCDTBT:PC 70 BM and perovskite thin film solar cells show changes in device capacitance when V dev approaches V bi . To account for the DC voltage loss across the load resistance, the relations between the applied circuit voltage V appl and the measured voltage drop V dev across the PCDTBT:PC 70 BM, neat PCDTBT, and perovskite thin-film devices are depicted in Figure 3b. On the other hand, Figure 3c shows the ΔV max at short-circuit, as obtained from the voltage transients, plotted as a function of laser pulse fluence, and compared for all three thin-film solar cells. We took great care to avoid high laser pulse fluences (which induce substantial bimolecular recombination) when recording the voltage transients at different V dev . The red solid line in Figure 3c is a guide to the eye with a slope of 1, indicating the absence of higher-order (e.g., bimolecular) recombination processes. The corresponding ITCE voltage transients for the PCDTBT:PC 70 BM, neat PCDTBT, and perovskite solar cell are shown in Figure 3d−f, from which ΔV max was obtained at the voltage plateaus.
From the C−V curves and voltage transients we calculated the EGE, which was determined based on the photogenerated charge carrier density (n ph ) and the pulse photon density (N ph )  We note, however, that due to expected nonuniform electric fields and uncertainties in the measured device capacitance at high voltages (i.e., when V dev approaches the built-in voltage), the trustable EGE regime in ITCE is limited to V dev below ∼0.66 V in the forward bias direction. This is partly due to the rapid increase of the capacitance with voltage (see Figure 3a), where the value of C becomes more sensitive to small voltage fluctuations (ΔV max ) and partly due to strong recombination and space charge effects affecting the measured capacitance at large bias.
In a similar manner, we investigated the EGE in a thin-film perovskite solar cell (see Figure 4b), where we find the EGE to be field-independent. Again, our ITCE results (red symbols) show good agreement with those obtained via TDCF. Similar to the PCDTBT:PC 70 BM device, the trustable V dev window is, when probed by ITCE, limited to ∼0.64 V in forward bias direction. We note that perovskites are quite different to organic semiconductors in that they are predominantly nonexcitonic at room temperature and thus demonstrate a more general (if not universal) applicability of ITCE to thinfilm photovoltaic devices.
Finally, we investigated a system with an electric fielddependent EGE. To this end, a neat PCDTBT thin-film device was used. It is well-established that single-component organic solar cells exhibit field dependent charge generation. 41,42 Therefore, a neat PCDTBT device is an appropriate model system to observe the field dependence. We note that the capacitance of this device showed a weaker voltage dependence (see Figure 3a), allowing for the capacitance to be accurately measured over the entire voltage range. Subsequently, as shown in Figure 4c, the field-dependent EGE results obtained via ITCE (red symbols) and TDCF (orange symbols) are in excellent agreement over the entire bias voltage regime.
In contrast to the PCDTBT:PC 70 BM and perovskite devices, the accuracy of the neat PCDTBT C−V measurement at large forward bias voltages was not influenced by carrier diffusion and back-injection from the electrodes into the photoactive layer; this can mainly be attributed to the nonohmic injection character of one or both of the electrodes, suppressing strong recombination and space charge effects at large voltages. In this regard, it should be noted that the EGE is a property of the photoactive layer, hence a modification of the device stack aimed at a more precise C−V measurement (or, suppression of diffusion of injected dark charges, recombination, and the buildup of space charge) allows for accurate ITCE measurements over the entire voltage regime.

■ CONCLUSIONS
We have presented a transient measurement technique, ITCE, to probe charge generation efficiency in thin-film solar cells, which is based on the sensitive measurement of pulsed, photoinduced changes in voltage drop across the active layer, combined with capacitance measurements. A simple seriescircuit with large RC-time is used to generate voltage transients at low laser pulse fluence from which the maximum change in active layer voltage drop can be determined. We derived and verified the theoretical framework of ITCE by DD simulations and demonstrated its applicability by probing the field dependence of EGE in thin-film perovskite and organic solar cells. Our results are in good agreement with those obtained via TDCF conducted on the same devices.
Despite the limitations of ITCE at high forward bias voltages due to uncertainties in the accurate measurement of the device capacitance, ITCE operates at very low pulse fluence (avoiding higher-order recombination) and does not suffer from RC-time limitations. Hence, ITCE with its much simpler circuit allows the measurement of small charge carrier densities sensitively and can be used in a complementary manner with the more complex TDCF method to probe the field dependence of charge generation in thin film solar cells.